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The Mathematics of Cryptography and Cybersecurity introduces students to the mathematical principles that secure digital communication in the modern world. The course focuses on the theory and construction of public-key cryptosystems and digital signature schemes, emphasizing the number-theoretic foundations of data security. Students will explore how mathematical ideas such as modular arithmetic, prime factorization, and discrete logarithms underpin real-world cybersecurity protocols including RSA, Diffie–Hellman key exchange, and elliptic curve cryptography. In addition to classical and modern cryptographic systems, the course highlights the role of mathematics in assessing vulnerabilities, analyzing security guarantees, and understanding emerging cryptographic challenges in cybersecurity. Topics include primality testing, factorization algorithms, probability and information theory, and collision resistance. This course offers a rigorous yet accessible path for students in mathematics and computer science to understand how abstract theory translates into the protection of information in a digital age.